Abstract

Quantum networks will enable a variety of applications, from secure communication and precision measurements to distributed quantum computing. Storing photonic qubits and controlling their frequency, bandwidth, and retrieval time are important functionalities in future optical quantum networks. Here we demonstrate these functions using an ensemble of erbium ions in yttrium orthosilicate coupled to a silicon photonic resonator and controlled via on-chip electrodes. Light in the telecommunication C-band is stored, manipulated, and retrieved using a dynamic atomic frequency comb protocol controlled by linear DC Stark shifts of the ion ensemble’s transition frequencies. We demonstrate memory time control in a digital fashion in increments of 50 ns, frequency shifting by more than a pulse width (${\pm}39\;{\rm MHz} $), and a bandwidth increase by a factor of 3, from 6 to 18 MHz. Using on-chip electrodes, electric fields as high as 3 kV/cm were achieved with a low applied bias of 5 V, making this an appealing platform for rare-earth ions, which experience Stark shifts of the order of 10 kHz/(V/cm).

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Optical quantum memories will enable long-distance quantum communication using quantum repeater protocols [13]. A quantum memory device that can control the bandwidth and frequency of stored light is additionally useful, as it can interface between optical elements that have different optimal operating points. Erbium-doped materials are a promising solid-state platform for ensemble-based optical quantum memories because of their long-lived optical transition in the telecommunication C-band that is highly coherent at cryogenic temperatures [4,5]. This allows for integration of memory systems with low-loss optical fibers, opening up opportunities for repeaters over continental distances, as well as integration with silicon photonics [6,7], one of the most advanced platforms for integrated photonics. Spin transitions in $^{167}{{\rm Er}^{3 +}}$-doped yttrium orthosilicate ($^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$) have also been shown to have long relaxation and coherence lifetimes at cryogenic temperatures and high magnetic fields [8], which opens the possibility for long-term spin-wave memories.

There have been several demonstrations of optical storage in erbium-doped materials [914], including storage at the quantum level [9,10,14] and on-chip storage [10,14]. These results are part of a larger body of optical quantum memory research [3,15] using rare-earth-ion-doped crystals [1619], atomic gases [20,21], and single atoms or defects [22,23]. In parallel with efforts to increase the efficiency [20] and storage time [18,19] of quantum memories, several works have focused on new types of multifunctional devices [2427] in which control fields are used to modify the state of the light during storage.

In many quantum repeater protocols [28], quantum memories act as interfaces between emitters such as quantum dots [29] or individual atoms [7]. Dynamic control of the optical pulses stored in these memories can correct for differences between individual emitters, leading to higher indistinguishably for Bell state measurements at the entanglement swapping stage of quantum repeater protocols [1]. In addition, with control over the frequency of stored light, one can map an input mode to a different output mode in a frequency multiplexed quantum memory, which enables quantum networks with fixed-time quantum memories [30].

In this work, we use a silicon resonator evanescently coupled to $^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$ ions and gold electrodes to realize a multifunctional on-chip device that can not only store light but also dynamically modify its frequency and bandwidth. Electrodes create a DC electric field that can be rapidly switched, which enables control of the $^{167}{{\rm Er}^{3 +}}$ ions’ optical transition frequency via the DC Stark shift [31]. Using a resonator increases the interaction between light and the ion ensemble, allowing on-chip implementation of the atomic frequency comb (AFC) memory protocol [32]. This protocol allows multiplexing in frequency, which offers a significant advantage in quantum repeater networks [33]. Additionally, the on-chip electrodes are patterned close together to achieve the high electric fields required for Stark shift control with CMOS-compatible applied voltages. We demonstrate dynamic control of memory time in a digital fashion as well as modification of the frequency and bandwidth of stored light.

 figure: Fig. 1.

Fig. 1. Multifunctional quantum storage device. (a) Schematic of device functionality showing the optical resonator (pink), electrodes (blue and red), and memory output. (b)–(d) Hybrid optical resonator comprised of an amorphous silicon ($\alpha {\rm Si}$) waveguide on $^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$ with photonic crystal mirrors on either end. (b) Cross section of waveguide (black outline) showing 2D finite element simulation of the TM waveguide mode. The purple-white gradient indicates the ${E_z}$ component of the optical field. (c) Band diagram showing waveguide mode (solid red line), band gap of a photonic crystal mirror (solid blue lines), and the design frequency of 195 THz (dashed red line). Blue areas indicate the ${{\rm Y}_2}{{\rm SiO}_5}$ light cone containing extended modes propagating in bulk ${{\rm Y}_2}{{\rm SiO}_5}$ (both sides for photonic crystal, left side only for waveguide). (d) Scanning electron micrograph showing a grating coupler and photonic crystal mirror including tapered sections on either side to reduce scattering [34]. (e)–(g) 3D finite element simulation of on-chip electrodes. (e)–(f) 2D slice at $z = 0$ showing electric potential (blue-red gradient) in the (e) parallel and (f) quadrupole biasing configurations. (g) Electric field ${E_y}(x)$ along the optical resonator in the parallel (green solid line) and quadrupole (orange solid line) configurations; ${E_y}(x)$ was measured at $z = 0$, $y = 0$, ${-}56\,\unicode{x00B5}{\rm m} \lt x \lt 56\,\unicode{x00B5}{\rm m}$ [green and orange lines in (e) and (f)]; dashed lines indicate ideal parallel (green) and quadrupole (orange) electric field distributions. (h) Optical micrograph showing an optical resonator, gold electrodes, and gold wires for electrical contact.

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2. HYBRID αSi-167Er3+: Y2SiO5 RESONATOR WITH ELECTRODES

The multifunctional device consists of an optical resonator coupled to $^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$ ions between gold electrodes. Using the AFC quantum storage protocol [35] and the ions’ Stark shift, light can be stored and manipulated in this device. Figure 1(a) shows a schematic of the device and the three functionalities demonstrated in this work: memory time control, frequency control, and bandwidth control. Different electric field configurations are created by applying a positive (blue) or negative (red) bias to each electrode. For the true device dimensions, see the micrograph in Fig. 1(h).

The optical resonator used in this work is a Fabry–Perot resonator comprised of a 100 µm amorphous silicon ($\alpha$Si) waveguide on $^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$ with photonic crystal mirrors on either end. Figures 1(b)–1(d) show simulations and micrographs of this resonator. The waveguide is $h = 310\,{\rm nm}$ tall and $w = 605\,{\rm nm}$ wide. Ten percent of the energy of the transverse-magnetic (TM) optical waveguide mode penetrates into the $^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$ and evanescently couples to the $^{167}{{\rm Er}^{3 +}}$ ions. Photonic crystal mirrors on either side are formed by a repeating pattern of elliptical air holes in the $\alpha$Si waveguide with period ${a_ \circ} = 370\,{\rm nm}$. A grating coupler is used to couple light from a free-space mode into and out of the resonator. The amorphous silicon resonator is fabricated on top of an $^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$ chip using a deposition and etching process similar to Ref. [6]. The $^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$ substrate is doped with isotopically purified $^{167}{{\rm Er}^{3 +}}$ ions at 135 ppm, measured by secondary ion mass spectrometry, and cut perpendicular to the ${D_1}$ crystal axis, such that the electric field of the TM optical mode is polarized along this axis. The $x$, $y$, and $z$ axes in Fig. 1 correspond to the ${D_2}$, $b$, and ${D_1}$ ${{\rm Y}_2}{{\rm SiO}_5}$ crystal axes, respectively.

Quality factors of up to ${10^5}$ were measured for weakly coupled resonators, where the photonic crystal mirrors on both sides were designed to be highly reflective. The device used in this work is made one-sided for more efficient quantum storage [14,35] by using fewer photonic crystal periods in one mirror to make it less reflective. Light is sent into and measured from the side with the lower-reflectivity mirror. The intrinsic quality factor for this device is also lower than the weakly coupled resonators, leading to a quality factor of $3 \times {10^4}$ and a coupling ratio of ${\kappa _{{\rm in}}}/\kappa = 0.2$, where ${\kappa _{{\rm in}}}$ is the coupling rate through the lower-reflectivity mirror and $\kappa$ is the total decay rate [36]. The lower- (higher-)reflectivity mirror consists of 6 (30) regularly spaced holes, with an additional 15 holes in the tapers on either side. Several one-sided devices with different numbers of regularly spaced holes on the lower-reflectivity side were fabricated on the same chip, and the device with the best combination of quality factor and ${\kappa _{{\rm in}}}/\kappa$ was chosen.

Electrodes are used to apply electric fields to those ions coupled to the optical resonator. There are four independently biased gold electrodes, each comprised of a $70\;\unicode{x00B5}{\rm m}$ diameter circle connected to a $20\,\unicode{x00B5}{\rm m} \times 60\,\unicode{x00B5}{\rm m}$ rectangle. They are patterned onto the $^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$ after the $\alpha$Si resonators using electron-beam lithography followed by electron-beam gold evaporation and liftoff. Figures 1(e)–1(g) show simulations of the two electrode biasing configurations: parallel, which applies a nearly constant electric field to all ions ($E(x) = a$), and quadrupole, which applies an electric field gradient along the resonator [approximating $\frac{{{\rm d}E(x)}}{{{\rm d}x}} = b$], where $a$ and $b$ are constants. The electrode geometry was designed to best approximate these two electric field profiles with four independently biased electrodes, while providing a large electric field for a given applied bias ($E/V$). In the $^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$ region where ions are coupled to the optical mode, the ${E_y}$ component of the electric field is dominant (${E_y} \gg {E_x},{E_z}$), and it does not vary significantly in the $z$ and $y$ directions. Therefore, only ${E_y}(x)$, which is aligned to the $b$ axis of the ${{\rm Y}_2}{{\rm SiO}_5}$ crystal, is considered.

The device is thermally connected to the coldest plate of a dilution refrigerator, the temperature of which is ${\sim}100\;{\rm mK}$. A static magnetic field of 0.98 T is applied along the ${{\rm Y}_2}{{\rm SiO}_5}$ ${D_1}$ axis with a superconducting electromagnet. Trim coils are used to cancel any magnetic field component along the $b$ axis. Two function generators with 120 MHz bandwidth and a total of four channels were used to apply pulses with amplitudes up to ${\pm}5\;{\rm V}$ to the electrodes. The remainder of the measurement setup was similar to the one described in Ref. [14].

3. DC STARK SHIFT IN 167Er3+: Y2SiO5

${{\rm Er}^{3 +}}$: ${{\rm Y}_2}{{\rm SiO}_5}$ has been extensively studied for quantum applications [4,5,7,1114,37,38], including demonstrations of AFC storage [12,14]. Erbium ions are substituted for yttrium ions in ${{\rm Y}_2}{{\rm SiO}_5}$ in two crystallographic sites, each of which has four different orientations due to the $C_{2h}^6$ crystal symmetry [39]. In this work, we use crystallographic site 2, which has an optical transition near 1539 nm [4]. $^{167}{{\rm Er}^{3 +}}$ has a nuclear spin $I = 7/2$, which, together with an effective electron spin, leads to 16 hyperfine levels in both the optical ground and excited states. At high fields and low temperatures, the electron spin is frozen, allowing the lowest eight ground-state hyperfine levels to be long lived [8,14], thereby enabling the spectral hole burning that is required to create atomic frequency combs. Aligning the magnetic field with the ${D_1}$ crystal axis enhances this effect because the ground-state electron $g$-tensor of $^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$ is nearly maximized in that direction for site 2 [39].

Dynamic control is enabled by the DC Stark shift. When a rare-earth ion in a crystal interacts with a DC electric field $\vec E$, its optical transition frequency is shifted due to the difference between the permanent electric dipole moments in the optical excited and optical ground states $\delta \vec\mu= {\vec\mu_{\rm e}} - {\vec\mu_{\rm g}}$. For non-centrosymmetric sites such as the yttrium sites in ${{\rm Y}_2}{{\rm SiO}_5}$, for which ${{\rm Er}^{3 +}}$ ions substitute, the linear Stark shift term $\delta f = - \frac{1}{h} \delta \vec\mu\cdot \mathop L\limits^ \leftrightarrow \cdot \vec E$ dominates, where $\mathop L\limits^ \leftrightarrow$ is the local field correction tensor [31].

The Stark shift is dependent on the orientation of the applied field relative to $\delta \vec\mu$ [40]. Without knowing $\delta \vec\mu$ or $\mathop L\limits^ \leftrightarrow$, the Stark shift can be empirically characterized for an electric field applied in a particular direction $\hat n$ ($\hat n$ is a unit vector) using the Stark shift parameter ${s_{\hat n}}$ given $\delta f = {s_{\hat n}}{E_{\hat n}}$. We measured ${s_{\hat n}} = 11.8 \pm 0.2$ kHz/(V/cm) for $\hat n$ nominally aligned with the ${{\rm Y}_2}{{\rm SiO}_5}$ crystal $b$ axis (see Supplement 1 Section 1).

In an ensemble of $^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$ ions, four different Stark shifts will be observed for an arbitrary electric field due to the four orientations of each crystallographic site [39]. For electric fields parallel or perpendicular to the $b$ axis, the Stark shifts of the four subclasses are pairwise degenerate, resulting in two Stark shifts $\delta {f_ \pm} = \pm sE$. In this work, all electric fields are applied parallel to the $b$ axis, so we will simply refer to two $^{167}{{\rm Er}^{3 +}}$ subclasses.

4. ATOMIC FREQUENCY COMB STORAGE WITH DYNAMIC MEMORY TIME CONTROL

After a photon is absorbed by an ensemble of ions, the ensemble of ions is described by a Dicke state [35]

$$\left| \Psi \right\rangle = \sum\limits_{j = 1}^{{N_{{\rm ions}}}} {c_j} {e^{i2\pi \left({{f_j} + \delta {f_j}(t)} \right) t}} {e^{- ik{{\vec r}_j}}}\left| {{{0 \ldots 1}_j}{{ \ldots 0}_N}} \right\rangle .$$

Each ion has a different transition frequency ${f_j}$ and position ${\vec r_j}$. For AFC storage, the transition frequencies $\{{f_j}\}$ form a frequency comb with period $\Delta$. When a photon is absorbed at $t = 0$, the ensemble of ions first dephase then rephase every $t = \frac{m}{\Delta}$, $m \in \mathbb{N}$, leading to a coherent reemission of the light [35]. A Stark shift $\delta {f_j}(t)$ enables dynamic control of light stored in the AFC by changing the optical transition frequencies of the ions. $\delta {f_j}(t)$ can be varied over time by changing the amplitude of the applied electric field (slowly relative to optical frequencies). This enables two types of control: electric field pulses applied between the absorption and emission of light modify the phase of the output, while electric field pulses applied during emission of light modify the frequency profile of the output light.

To achieve dynamic control of storage time, the electrodes are biased in a parallel configuration as shown in the top panel of Fig. 1(a). When an electric pulse is applied, the two $^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$ subclasses experience opposite frequency shifts ${\pm}\delta f(t) = \pm {s_b}E$. By appropriately choosing the length in time $t$ and amplitude $E$ of the electric pulse, a $\pi$ phase difference between subclasses can be introduced: $\pi = 2\pi \times (+ {s_b}E - (- {s_b}E)) \times t$, which will prevent any coherent emission from the ensemble. An equal-area electric pulse with opposite sign can then rephase the two subclasses, and it allows coherent reemissions from the AFC. This procedure of dephasing and rephasing the ensemble works even if the electric field distribution is not perfectly homogeneous, as shown in the context of Stark echo modulation memory in Reference [41]. Recently, dynamic control of memory time in AFC was demonstrated using this same procedure in ${{\rm Pr}^{3 +}}$: ${{\rm Y}_2}{{\rm SiO}_5}$ [42]. Reference [12] proposed a similar protocol but using an electric field gradient.

 figure: Fig. 2.

Fig. 2. AFC storage with dynamic memory time control. (a) Pulse sequence (not to scale, details in main text). (b) Atomic frequency comb. Cavity reflectance (black points) and fit to six Gaussians (solid black lines). All teeth are fit together, with the finesse fixed to the value from (d). Detuning is measured from 194,822 GHz. The gray Gaussian with a dashed outline represents the input pulses in frequency space. c) Emission of stored light at different times ${t_{{\rm memory}}} = \frac{m}{\Delta}$. Partly reflected input pulse are shown in gray at $t = 0$. On-demand memory outputs are shown in blue (darkest shade). Subsequent emissions (green to red) are discussed in the main text. Electric pulses are not shown. (d) Energy emitted in the time bin at $t = \frac{m}{\Delta}$ for each value of $m$. Black data points represent the normalized counts when all previous emissions are suppressed with electric pulses [blue pulses in (c)]. Gray data points represent normalized counts when previous emissions are not suppressed, meaning no electric pulses are used [all pulses on line $m = 1$ in (c)]. The error bars, representing $\sqrt {{N_{{\rm counts}}}}$, are smaller than the markers. The solid line is a fit to theory, fitting only for comb finesse.

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The pulse sequence used to achieve dynamic control of AFC storage is shown in Fig. 2(a). Not shown is the initialization to move most of the population into one hyperfine state, which is performed before every experiment (see Supplement 1 Section 2 and Refs. [8,14]). First, an AFC with period $\Delta$ is created by repeatedly burning away the population between the teeth of the comb, ${n_{{\rm comb}}} = 20$ times. Then an input pulse indicated by the red laser pulse is sent into the resonator at $t = 0$ and is absorbed by the AFC. Shown in light red are possible emissions corresponding to rephasing events of the AFC at times $t = \frac{m}{\Delta}$. Without electric field control, the output of the memory (the first and largest emission) would be centered at $t = \frac{1}{\Delta}$ ($m = 1$). The schematic shows instead an emission in red at $t = \frac{3}{\Delta}$ ($m = 3$), obtained when a first electric pulse is applied before the first emission and a compensating pulse is applied immediately before the third emission.

Figure 2(b) shows the AFC used in this experiment. The period of the comb, extracted from the fit, is $19.7 \pm 0.1\;{\rm MHz} $, which corresponds to a minimum storage time of $t = \frac{1}{\Delta} = 50\;{\rm ns}$. Figure 2(c) shows dynamically controlled storage for various values of $m$. The input pulse is a weak coherent pulse corresponding to an average photon number in the resonator of $\left\langle {{n_{{\rm cav}}}} \right\rangle = 1.9$. Two electric pulses were used to control memory time. The first was a 10 ns long pulse with amplitude 2 kV/cm centered at ${t_{{\rm pulse} {1}}} = 25$ ns. The second was 10 ns long with an opposite amplitude of -2 kV/cm, and its center position was varied as ${t_{{\rm pulse} {2}}} = 25\;{\rm ns} + (m - 1) \times 50\;{\rm ns}$ to allow the emission at ${t_{{\rm memory}}} = \frac{m}{\Delta}$. The electric pulses were calibrated to ensure optimal suppression of the emission (see Supplement 1 Section 3). Between the two electric pulses, emission was suppressed down to the dark counts level, a factor of 100 lower than peak emission counts. For the $m = 1$ case, no electric pulses were applied. The presence of multiple smaller pulses following the output pulse is a feature of the high finesse and low efficiency of the memory (see Supplement 1 Section 4). For higher-efficiency, high-finesse AFCs, subsequent emissions are significantly suppressed [42].

Figure 2(d) shows the energy emitted in the $m $th time bin for ${t_{{\rm memory}}} = \frac{m}{\Delta}$. The data is fit to the dephasing term in the theoretical storage efficiency for a comb with Gaussian teeth: ${\rm exp}({- \frac{{{\pi ^2}}}{{2{\rm ln}2}}\frac{{{m^2}}}{{{F^2}}}})$ [12,35], where $F = \Delta /\gamma$ is the comb finesse and $\gamma$ is the full width at half-maximum (FWHM) of each tooth. The $m = 1$ data point is excluded from the fit because the approximately 100 ns dead time of the single photon detector after the input pulse is thought to lead to undercounting in that time bin. A comb finesse of $F = 12.2 \pm 0.2$ ($\gamma = 1.6\;{\rm MHz} $) is extracted from this fit. This corresponds to a $1/e$ point of 240 ns ($m = 4$ for digital storage time). To improve on this scaling requires a smaller tooth width $\gamma$. The gray data in Fig. 2(d) show the total counts in the $m$th time bin when the previous output pulses are not suppressed.

5. DYNAMIC FREQUENCY CONTROL

The frequency of light stored in an AFC can be dynamically modified during emission. The atomic frequency comb is shifted in frequency during the emission of stored light by biasing the electrodes in the parallel configuration as shown in the middle panel of Fig. 1(a). The pulse sequence used to achieve AFC storage with frequency control is shown in Fig. 3(a). The first step is to eliminate one of the two $^{167}{{\rm Er}^{3 +}}$ subclasses from the spectral window, leaving only ions that experience a positive Stark shift $\delta {f_ +} = + {s_b}E$ (the choice of subclass is arbitrary). This is accomplished using a two-part comb burning procedure. With the first burning step, a normal AFC containing both subclasses is created using a sequence of laser pulses. For the second burning step, the two subclasses are split by $\Delta /2$ using a parallel electric field, and a similar sequence of laser pulses is used, but with a frequency shift of $\Delta /4$. This burns away ions with a negative shift $\delta {f_ -} = - {s_b}E$.

 figure: Fig. 3.

Fig. 3. AFC storage with frequency control. (a) Pulse sequence (not to scale; details in main text). (b)–(c) Examples of AFC output pulses with (green, lighter) and without (blue, darker) a frequency shift. The filled-in area is a Gaussian fit to the data (circles). Detuning is measured from 194,822 GHz. Frequency shifts of (b) 9 MHz and (c) 30 MHz are shown. (d) The output detuning as a function of electric field applied during emission. Circles are the centers of Gaussian fits [as shown in (b)–(c)]. The error bars, which are smaller than the markers, are 95% confidence intervals for those fits. The solid line is a linear fit to the data, yielding a slope of $13.0 \pm 0.3$ kHz/(V/cm), similar to the Stark shift value measured by hole-burning spectroscopy (see Supplement 1 Section 1).

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Repeating the comb burning procedure ${n_{{\rm comb}}} = 5$ times, an AFC with width 145 MHz and a period $\Delta = 5\;{\rm MHz} $ is created. An input pulse is sent in, and the rephasing of the AFC causes an emission at $t = \frac{1}{\Delta} = 200\;{\rm ns}$. During this emission, an electric field pulse with amplitude ${E_{{\rm pulse}}}$ applied in the parallel configuration will cause the ions to emit with a frequency shift of $f = + {s_b}{E_{{\rm pulse}}}$. Figures 3(b) and 3(c) show the light emitted from the memory, with and without a frequency shift. A heterodyne measurement is used to measure the frequency of the output pulse directly. To detect the output pulse with this lower-sensitivity detection method, bright input pulses were used $({\left\langle {{n_{{\rm cav}}}} \right\rangle = 46 \times {{10}^3}})$. Figure 3(d) shows the linear frequency shift as a function of electric field. The decrease in output amplitude with frequency shift evident in Figs. 3(b) and 3(c) is mainly due to the broadening of the teeth width, which is caused by inhomogeneity of Stark shifts experienced by the ions (see Supplement 1 Section 1). This broadening results in a decrease in efficiency via the dephasing term introduced in the previous section.

 figure: Fig. 4.

Fig. 4. AFC storage with bandwidth control. (a) Pulse sequence (not to scale; details in main text). (b) AFC storage with (bottom) and without (top) bandwidth broadening. Colored areas are Gaussian fits to photon counts data (circles) from which widths are extracted. The partially reflected input pulse with FWHM 77.4 ns (5.7 MHz FWHM in the frequency domain) is shown in gray (lighter color) in both traces at $t = 0$, demagnified by a factor of ${10^3}$. The top trace shows the case without bandwidth broadening ${E_{{\rm max}}}(t = 630\,{\rm ns}) = {E_{{\rm max}}}(t = 0) = 0.67\;{\rm kV/cm}$, where the width of the output (blue, darker) is $77.1 \pm 2.0\;{\rm ns}$ ($5.7 \pm 0.1\;{\rm MHz} $). The bottom trace shows the maximum bandwidth broadening ${E_{{\rm max}}}(t = 630\,{\rm ns}) = 4 \times {E_{{\rm max}}}(t = 0) = 2.8\;{\rm kV/cm}$, where the width of the output (blue, darker) is $24.3 \pm 0.5\;{\rm ns}$ ($18.1 \pm 0.4\;{\rm MHz} $). Insets show schematics of electrode pulse sequences. (c) Bandwidth of pulses as a function of the $E_{{\rm max}}^{{\rm output}}$. In all cases, $E_{{\rm input}}^{{\rm max}} = 0.67\;{\rm kV/cm}$. Filled black circles are FWHM data. The error bars, which are smaller than the markers, represent 95% confidence intervals from fits. The unfilled gray circles are simulation data (see main text and Supplement 1 Section 5).

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6. DYNAMIC BANDWIDTH CONTROL

The bandwidth of stored light can be dynamically controlled by biasing the electrodes in a quadrupole configuration as shown in the bottom panel of Fig. 1(a). In the quadrupole configuration, electric pulses create a gradient electric field across the ions so that each ion experiences a different Stark shift. Figure 4(a) shows the pulse sequence used to achieve AFC storage with bandwidth control. First, an AFC with $\Delta = 1.6\;{\rm MHz} $ and bandwidth 144 MHz is created by repeatedly burning away population ${n_{{\rm comb}}} = 20$ times. Next, an input pulse $({\left\langle {{n_{{\rm cav}}}} \right\rangle = 1.9})$ is sent into the device, leading to an output pulse at $t = \frac{1}{\Delta} = 630\;{\rm ns}$. A gradient field applied during the AFC emission causes the bandwidth of the absorbing ion ensemble to broaden, such that the emitted pulse is also broader in frequency relative to the input pulse. However, the gradient field also alters the phase evolution of each ion by changing its resonant frequency. If not compensated, the different phases accumulated across ions in the ensemble could prevent emission altogether. For this reason, three electric pulses are applied during the input and output optical pulses and also during the wait time. These three pulses have the same area but can have different amplitudes. The first and second pulses are used to add phase compensation such that the net electric-field-induced phase shift is zero for each ion, accounting for the fact that AFC storage is first-in-first-out [24,43].

Figure 4(b) shows AFC storage with no broadening (top) and with the maximum achieved bandwidth broadening (bottom). A broadening in frequency space is seen as a narrowing of the output pulse in time. By fitting the output pulses to Gaussians, the temporal FWHMs ($\Delta t$) of input and output pulses are extracted and converted to bandwidth or frequency FWHMs ($\Delta f$) using $\Delta f = \frac{{4{\rm ln}2}}{{2\pi}}{(\Delta t)^{- 1}}$. Figure 4(c) shows the trend of output bandwidth as a function of the maximum electric field applied during the third pulse ${E_{{\rm max}}}$ (the electric field across the resonator ranges from ${-}{E_{{\rm max}}}$ to ${E_{{\rm max}}}$). To confirm that the trend observed in the data is expected given the atomic frequency comb profile, the input pulse, and the electric field distribution ${E_y}(x)$, a simulation of the experiment was performed by numerically integrating the time-evolution equations of the atoms and cavity (see Supplement 1 Section 5). The simulation data reproduces the trend in FWHM as a function of field. The only previously unknown parameter used in this simulation was the distance that the optical mode penetrates into the photonic crystal mirrors, which modifies the effective resonator length and changes the value of ${E_{{\rm max}}}$. This parameter was found to be ${x_{{\rm eff}}} = 6\;\unicode{x00B5}{\rm m}$ for each mirror by coarsely sweeping ${x_{{\rm eff}}}$ in $1\;\unicode{x00B5}{\rm m}$ increments in the simulation to find the best fit to the data.

7. DISCUSSION

In this work, we have demonstrated the capabilities of an on-chip optical storage device with DC Stark shift control. Taking this technology on chip has two main advantages. First, it allows miniaturization and future integration with other optical components on chip. Second, it enables simple generation of large electric fields. Because the distance between electrodes across the resonator is small (a minimum of $20\;\unicode{x00B5}{\rm m}$), electric fields of 3 kV/cm are generated with just ${\pm}5 \; {\rm V}$ of applied bias in the parallel configuration. Such biases were easily supplied by a function generator with no additional amplification. In the quadrupole configuration, electric field gradients of up to $50\;{\rm V/cm}/\unicode{x00B5}{\rm m}$ were generated, corresponding to gradient of $0.58\;{\rm MHz}/\unicode{x00B5}{\rm m}$ in $^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$ transition frequencies.

For the dynamically controlled memory times in Fig. 2(d), an excellent match was found between the amplitude of stored light as a function of time and the theoretical limit due to the dephasing of a comb with finesse $F = 12.2$, indicating that the two electric field control pulses did not introduce any irreversible dephasing. This was also confirmed using a two-pulse photon echo measurement, where inserting two electric field pulses with equal area and opposite sign between the first and second optical pulses was found not to decrease the optical coherence time ${T_2}$, which was measured in this device to be $108 \pm 13\; \unicode{x00B5} {\rm s}$.

Frequency control was demonstrated for up to ${\pm}39\;{\rm MHz} $. In this work, the maximum shift was set by the maximum applied electric field of 3 kV/cm. One technical difficulty is that ions from the other subclass that are outside of the comb will act as an absorbing background when the comb is shifted in frequency and the other subclass experiences an opposite frequency shift. Assuming that the comb can be sufficiently separated in frequency from the other subclass using high electric fields, a more fundamental limit is set by the inhomogeneity of the Stark shifts, which leads to a decrease in storage efficiency with increasing frequency shift. In this device, the Stark shift inhomogeneity was dominated by an electric field distribution that was not perfectly homogeneous [see Fig. 1(g)]. Even in a perfectly homogeneous field, however, some inhomogeneity in Stark shifts will exist due to crystal field variations throughout the crystal [31].

The bandwidth of stored light was changed by a factor of 3 from 6 to 18 MHz. The maximum broadening demonstrated was limited by the maximum electric field gradient of $50\;{\rm V/cm}/\unicode{x00B5}{\rm m}$. With higher gradients, stored pulses could be broadened up to half the bandwidth of the comb, and the bandwidth of combs in this material is limited to ${\sim}150\;{\rm MHz} $ [14]. Decreasing the bandwidth of a stored pulse is not possible with this procedure because the AFC cannot be made narrower with a gradient electric field, only wider. Narrowing the AFC could be accomplished with a frequency-selective shift such as the AC Stark shift. The storage efficiency was observed to decrease when changing the bandwidth of the stored pulse. This decrease in efficiency, which was also seen in simulation, was stronger when the bandwidth change was larger, and it was not present when the three electric pulses had equal amplitude (corresponding to no change in pulse bandwidth).

An on-chip resonator allows for storage efficiencies approaching unity if the impedance matching condition is met [32]. In this device, the storage efficiency was up to 0.4%, depending on the finesse of the comb created, and it was limited by the low coupling between the ensemble of ions and the optical mode of the resonator, characterized by an ensemble cooperativity $C \lt 1$, and the small coupling ratio of the lower-reflectivity mirror ${\kappa _{{\rm in}}}/\kappa = 0.2$ (see efficiency discussion in Appendix D of Reference [14]). The storage time on an optical transition is ultimately limited by the optical coherence time ${T_2}$. However, in $^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$, superhyperfine coupling to yttrium nuclear spins in the crystal prevents the creation of narrow spectral features, which means a low storage efficiency for storage times longer than ${\sim}500\;{\rm ns}$ [14]. Superhyperfine coupling is a major limitation to high-efficiency long-lived storage in $^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$ when using memory protocols based on spectral tailoring such as AFC.

For quantum repeater applications, the efficiency and duration of on-chip storage must be improved. The storage efficiency in hybrid $\alpha {{\rm Si}–^{167}}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$ devices can be increased by using thinner silicon to increase the fraction of the optical mode energy in the $^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$, which would increase the ensemble cooperativity, and by optimizing the resonator nanofabrication procedure to decrease scattering and absorption loss in order to achieve higher intrinsic quality factors. For example, using crystalline silicon could mitigate absorption loss. Higher intrinsic quality factors would increase both the ensemble cooperativity and the coupling ratio ${\kappa _{{\rm in}}}/\kappa$, both of which affect storage efficiency. To overcome the superhyperfine limit to storage time, creative solutions such as using clock transitions in $^{167}{{\rm Er}^{3 +}}$:${{\rm Y}_2}{{\rm SiO}_5}$ [38,44,45], which are less sensitive to superhyperfine coupling, or finding new crystal hosts for erbium ions can be used. Longer storage times can also be realized by combining AFC storage with spin-wave storage, where the optical excitation is reversibly transferred to a hyperfine level [35]. Spin-wave storage could be combined with the bandwidth and frequency control demonstrated here, and it would eliminate the need for memory time control with electric fields. Another requirement of quantum memories is to store quantum states of light with high fidelity. This has already been demonstrated with the AFC protocol [9]. Storage of weak coherent states using the AFC protocol with DC Stark shift control of storage time has also been recently demonstrated [42]. Future work should include demonstrations of on-chip storage of light at the quantum level with dynamic frequency and bandwidth control. More generally, this type of device could work with different absorbers that experience linear Stark shifts, or with other quantum storage protocols that do not require spectral tailoring such as Stark echo modulation memory [41].

The functionality of the device is not limited to the demonstrations in this work. For example, a gradient field could be used instead of a homogeneous field to dynamically control the storage time. The bandwidth or frequency of emissions at any time $t = \frac{m}{\Delta}$ could be modified, frequency and bandwidth control could be combined, and the order of two pulses could be reversed. A device that enables Stark shift control of an ion’s transition frequency is useful for other technologies as well. For example, a gradient electric field could be used to tune two $^{167}{{\rm Er}^{3 +}}$ ions coupled to the same resonator into resonance with one another. This would enable entangling gates between the two ions, a key step in quantum repeater protocols using single ions [46].

8. CONCLUSION

In this work we demonstrated a multifunctional on-chip device that can store light while dynamically modifying its storage time, frequency, and bandwidth. Dynamic control of the memory time and the frequency profile of the output light was achieved via the linear DC stark shift of $^{167}{{\rm Er}^{3 +}}$ ions in ${{\rm Y}_2}{{\rm SiO}_5}$. We demonstrated dynamic control of memory time in a digital fashion with storage times that were multiples of 50 ns, for up to 400 ns. The frequency of stored light was changed by up to ${\pm}39\;{\rm MHz} $, and the bandwidth of stored light was increased by up to a factor of 3, from 6 to 18 MHz. This on-chip platform, comprising a resonator evanescently coupled to an ensemble of atoms that experience a DC Stark shift and on-chip electrodes, can be adapted to other materials and other quantum memory protocols.

Funding

Air Force Office of Scientific Research (FA9550-18-1-0374); National Science Foundation (EFRI 1741707); Natural Sciences and Engineering Research Council of Canada (PGSD2-502755-2017, PGSD3-502844-2017); American Australian Association (Northrup Grumman Fellowship).

Acknowledgment

We acknowledge Dimitrie-Calin Cielecki for help with electrode simulations, Phillip Jahelka for help with measuring the refractive index of amorphous silicon, Yunbin Guan for help with measuring the erbium concentration, and Andrei Ruskuc and Hirsh Kamakari for building the superconducting magnets for this experiment. I. C. and J. R. acknowledge support from the Natural Sciences and Engineering Research Council of Canada (Grants PGSD2-502755-2017 and PGSD3-502844-2017). J. G. B. acknowledges support from the American Australian Association’s Northrop Grumman Fellowship. During the preparation of this paper we became aware of similar work [47].

Disclosures

The authors declare no conflicts of interest.

 

See Supplement 1 for supporting content.

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References

  • View by:

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    [Crossref]
  27. O. Morin, M. Körber, S. Langenfeld, and G. Rempe, “Deterministic shaping and reshaping of single-photon temporal wave functions,” Phys. Rev. Lett. 123, 133602 (2019).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  38. J. V. Rakonjac, Y.-H. Chen, S. P. Horvath, and J. J. Longdell, “Long spin coherence times in the ground state and in an optically excited state of 163Er3+:Y2SiO5 at zero magnetic field,” Phys. Rev. B 101, 184430 (2020).
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2020 (6)

A. Holzäpfel, J. Etesse, K. T. Kaczmarek, A. Tiranov, N. Gisin, and M. Afzelius, “Optical storage for 0.53 s in a solid-state atomic frequency comb memory using dynamical decoupling,” New J. Phys. 22, 063009 (2020).
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M. K. Bhaskar, R. Riedinger, B. Machielse, D. S. Levonian, C. T. Nguyen, E. N. Knall, H. Park, D. Englund, M. Lončar, D. D. Sukachev, and M. D. Lukin, “Experimental demonstration of memory-enhanced quantum communication,” Nature 580, 60–64 (2020).
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Y. Wu, J. Liu, and C. Simon, “Near-term performance of quantum repeaters with imperfect ensemble-based quantum memories,” Phys. Rev. A 101, 042301 (2020).
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J. V. Rakonjac, Y.-H. Chen, S. P. Horvath, and J. J. Longdell, “Long spin coherence times in the ground state and in an optically excited state of 163Er3+:Y2SiO5 at zero magnetic field,” Phys. Rev. B 101, 184430 (2020).
[Crossref]

M. Businger, A. Tiranov, K. T. Kaczmarek, S. Welinski, Z. Zhang, A. Ferrier, P. Goldner, and M. Afzelius, “Optical spin-wave storage in a solid-state hybridized electron-nuclear spin ensemble,” Phys. Rev. Lett. 124, 053606 (2020).
[Crossref]

F. K. Asadi, S. C. Wein, and C. Simon, “Protocols for long-distance quantum communication with single 167Er ions,” Quantum Sci. Technol. 5, 045015 (2020).
[Crossref]

2019 (6)

H. Wang, H. Hu, T.-H. Chung, J. Qin, X. Yang, J.-P. Li, R.-Z. Liu, H.-S. Zhong, Y.-M. He, X. Ding, Y.-H. Deng, Q. Dai, Y.-H. Huo, S. Höfling, C.-Y. Lu, and J.-W. Pan, “On-demand semiconductor source of entangled photons which simultaneously has high fidelity, efficiency, and indistinguishability,” Phys. Rev. Lett. 122, 113602 (2019).
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M. Mazelanik, M. Parniak, A. Leszczyński, M. Lipka, and W. Wasilewski, “Coherent spin-wave processor of stored optical pulses,” NPJ Quantum Inf. 5, 22 (2019).
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O. Morin, M. Körber, S. Langenfeld, and G. Rempe, “Deterministic shaping and reshaping of single-photon temporal wave functions,” Phys. Rev. Lett. 123, 133602 (2019).
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Y. Wang, J. Li, S. Zhang, K. Su, Y. Zhou, K. Liao, S. Du, H. Yan, and S.-L. Zhu, “Efficient quantum memory for single-photon polarization qubits,” Nat. Photonics 13, 346–351 (2019).
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I. Craiciu, M. Lei, J. Rochman, J. M. Kindem, J. G. Bartholomew, E. Miyazono, T. Zhong, N. Sinclair, and A. Faraon, “Nanophotonic quantum storage at telecommunication wavelength,” Phys. Rev. Appl. 12, 024062 (2019).
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M. F. Askarani, M. G. Puigibert, T. Lutz, V. B. Verma, M. D. Shaw, S. W. Nam, N. Sinclair, D. Oblak, and W. Tittel, “Storage and reemission of heralded telecommunication-wavelength photons using a crystal waveguide,” Phys. Rev. Appl. 11, 054056 (2019).
[Crossref]

2018 (3)

A. M. Dibos, M. Raha, C. M. Phenicie, and J. D. Thompson, “Atomic source of single photons in the telecom band,” Phys. Rev. Lett. 120, 243601 (2018).
[Crossref]

M. Rančić, M. P. Hedges, R. L. Ahlefeldt, and M. J. Sellars, “Coherence time of over a second in a telecom-compatible quantum memory storage material,” Nat. Phys. 14, 50–54 (2018).
[Crossref]

Y.-F. Hsiao, P.-J. Tsai, H.-S. Chen, S.-X. Lin, C.-C. Hung, C.-H. Lee, Y.-H. Chen, Y.-F. Chen, I. A. Yu, and Y.-C. Chen, “Highly efficient coherent optical memory based on electromagnetically induced transparency,” Phys. Rev. Lett. 120, 183602 (2018).
[Crossref]

2017 (1)

2016 (4)

K. Heshami, D. G. England, P. C. Humphreys, P. J. Bustard, V. M. Acosta, J. Nunn, and B. J. Sussman, “Quantum memories: emerging applications and recent advances,” J. Mod. Opt. 63, 2005–2028 (2016).
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D. Schraft, M. Hain, N. Lorenz, and T. Halfmann, “Stopped light at high storage efficiency in a Pr3+:Y2SiO5 crystal,” Phys. Rev. Lett. 116, 073602 (2016).
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K. A. G. Fisher, D. G. England, J.-P. W. MacLean, P. J. Bustard, K. J. Resch, and B. J. Sussman, “Frequency and bandwidth conversion of single photons in a room-temperature diamond quantum memory,” Nat. Commun. 7, 11200 (2016).
[Crossref]

A. Arcangeli, A. Ferrier, and P. Goldner, “Stark echo modulation for quantum memories,” Phys. Rev. A 93, 062303 (2016).
[Crossref]

2015 (2)

E. Saglamyurek, J. Jin, V. B. Verma, M. D. Shaw, F. Marsili, S. W. Nam, D. Oblak, and W. Tittel, “Quantum storage of entangled telecom-wavelength photons in an erbium-doped optical fibre,” Nat. Photonics 9, 83–87 (2015).
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G. Brennen, E. Giacobino, and C. Simon, “Focus on quantum memory,” New J. Phys. 17, 050201 (2015).
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2014 (2)

J. Dajczgewand, J.-L. L. Gouët, A. Louchet-Chauvet, and T. Chanelière, “Large efficiency at telecom wavelength for optical quantum memories,” Opt. Lett. 39, 2711–2714 (2014).
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N. Sinclair, E. Saglamyurek, H. Mallahzadeh, J. A. Slater, M. George, R. Ricken, M. P. Hedges, D. Oblak, C. Simon, W. Sohler, and W. Tittel, “Spectral multiplexing for scalable quantum photonics using an atomic frequency comb quantum memory and feed-forward control,” Phys. Rev. Lett. 113, 053603 (2014).
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2013 (2)

G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111, 033601 (2013).
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S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Highly efficient coupling from an optical fiber to a nanoscale silicon optomechanical cavity,” Appl. Phys. Lett. 103, 181104 (2013).
[Crossref]

2012 (1)

D. L. McAuslan, J. G. Bartholomew, M. J. Sellars, and J. J. Longdell, “Reducing decoherence in optical and spin transitions in rare-earth-metal-ion–doped materials,” Phys. Rev. A 85, 032339 (2012).
[Crossref]

2011 (2)

B. Lauritzen, J. Minář, H. de Riedmatten, M. Afzelius, and N. Gisin, “Approaches for a quantum memory at telecommunication wavelengths,” Phys. Rev. A 83, 012318 (2011).
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H. P. Specht, C. Nölleke, A. Reiserer, M. Uphoff, E. Figueroa, S. Ritter, and G. Rempe, “A single-atom quantum memory,” Nature 473, 190–193 (2011).
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2010 (4)

M. Afzelius and C. Simon, “Impedance-matched cavity quantum memory,” Phys. Rev. A 82, 022310 (2010).
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B. Lauritzen, J. Minář, H. de Riedmatten, M. Afzelius, N. Sangouard, C. Simon, and N. Gisin, “Telecommunication-wavelength solid-state memory at the single photon level,” Phys. Rev. Lett. 104, 080502 (2010).
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M. P. Hedges, J. J. Longdell, Y. Li, and M. J. Sellars, “Efficient quantum memory for light,” Nature 465, 1052–1056 (2010).
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I. Usmani, M. Afzelius, H. de Riedmatten, and N. Gisin, “Mapping multiple photonic qubits into and out of one solid-state atomic ensemble,” Nat. Commun. 1, 12 (2010).
[Crossref]

2009 (4)

T. Böttger, C. W. Thiel, R. L. Cone, and Y. Sun, “Effects of magnetic field orientation on optical decoherence in Er3+:Y2SiO5,” Phys. Rev. B 79, 115104 (2009).
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P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[Crossref]

M. Afzelius, C. Simon, H. de Riedmatten, and N. Gisin, “Multimode quantum memory based on atomic frequency combs,” Phys. Rev. A 79, 052329 (2009).
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M. Hosseini, B. M. Sparkes, G. Hétet, J. J. Longdell, P. K. Lam, and B. C. Buchler, “Coherent optical pulse sequencer for quantum applications,” Nature 461, 241–245 (2009).
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2008 (3)

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
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S. R. Hastings-Simon, B. Lauritzen, M. U. Staudt, J. L. M. van Mechelen, C. Simon, H. de Riedmatten, M. Afzelius, and N. Gisin, “Zeeman-level lifetimes in Er3+:Y2SiO5,” Phys. Rev. B 78, 085410 (2008).
[Crossref]

Y. Sun, T. Böttger, C. W. Thiel, and R. L. Cone, “Magnetic g tensors for the 4I15/2 and 4I13/2 states of Er3+:Y2SiO5,” Phys. Rev. B 77, 085124 (2008).
[Crossref]

2007 (2)

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multimode memories,” Phys. Rev. Lett. 98, 190503 (2007).
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R. M. Macfarlane, “Optical stark spectroscopy of solids,” J. Lumin. 125, 156–174 (2007), (Festschrift in Honor of Academician Alexander A. Kaplyanskii).
[Crossref]

2006 (1)

T. Böttger, Y. Sun, C. W. Thiel, and R. L. Cone, “Spectroscopy and dynamics of Er3+:Y2SiO5 at 1.5µm,” Phys. Rev. B 74, 075107 (2006).
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1998 (1)

H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[Crossref]

1997 (1)

F. R. Graf, A. Renn, U. P. Wild, and M. Mitsunaga, “Site interference in Stark-modulated photon echoes,” Phys. Rev. B 55, 11225–11229 (1997).
[Crossref]

Acosta, V. M.

K. Heshami, D. G. England, P. C. Humphreys, P. J. Bustard, V. M. Acosta, J. Nunn, and B. J. Sussman, “Quantum memories: emerging applications and recent advances,” J. Mod. Opt. 63, 2005–2028 (2016).
[Crossref]

Afzelius, M.

A. Holzäpfel, J. Etesse, K. T. Kaczmarek, A. Tiranov, N. Gisin, and M. Afzelius, “Optical storage for 0.53 s in a solid-state atomic frequency comb memory using dynamical decoupling,” New J. Phys. 22, 063009 (2020).
[Crossref]

M. Businger, A. Tiranov, K. T. Kaczmarek, S. Welinski, Z. Zhang, A. Ferrier, P. Goldner, and M. Afzelius, “Optical spin-wave storage in a solid-state hybridized electron-nuclear spin ensemble,” Phys. Rev. Lett. 124, 053606 (2020).
[Crossref]

B. Lauritzen, J. Minář, H. de Riedmatten, M. Afzelius, and N. Gisin, “Approaches for a quantum memory at telecommunication wavelengths,” Phys. Rev. A 83, 012318 (2011).
[Crossref]

B. Lauritzen, J. Minář, H. de Riedmatten, M. Afzelius, N. Sangouard, C. Simon, and N. Gisin, “Telecommunication-wavelength solid-state memory at the single photon level,” Phys. Rev. Lett. 104, 080502 (2010).
[Crossref]

I. Usmani, M. Afzelius, H. de Riedmatten, and N. Gisin, “Mapping multiple photonic qubits into and out of one solid-state atomic ensemble,” Nat. Commun. 1, 12 (2010).
[Crossref]

M. Afzelius and C. Simon, “Impedance-matched cavity quantum memory,” Phys. Rev. A 82, 022310 (2010).
[Crossref]

M. Afzelius, C. Simon, H. de Riedmatten, and N. Gisin, “Multimode quantum memory based on atomic frequency combs,” Phys. Rev. A 79, 052329 (2009).
[Crossref]

S. R. Hastings-Simon, B. Lauritzen, M. U. Staudt, J. L. M. van Mechelen, C. Simon, H. de Riedmatten, M. Afzelius, and N. Gisin, “Zeeman-level lifetimes in Er3+:Y2SiO5,” Phys. Rev. B 78, 085410 (2008).
[Crossref]

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multimode memories,” Phys. Rev. Lett. 98, 190503 (2007).
[Crossref]

Ahlefeldt, R. L.

M. Rančić, M. P. Hedges, R. L. Ahlefeldt, and M. J. Sellars, “Coherence time of over a second in a telecom-compatible quantum memory storage material,” Nat. Phys. 14, 50–54 (2018).
[Crossref]

Alqedra, M. K.

S. P. Horvath, M. K. Alqedra, A. Kinos, A. Walther, S. Kröll, and L. Rippe, “Noise free on-demand atomic-frequency comb quantum memory,” arXiv:2006.00943 (2020).

Arbabi, A.

Arcangeli, A.

A. Arcangeli, A. Ferrier, and P. Goldner, “Stark echo modulation for quantum memories,” Phys. Rev. A 93, 062303 (2016).
[Crossref]

Asadi, F. K.

F. K. Asadi, S. C. Wein, and C. Simon, “Protocols for long-distance quantum communication with single 167Er ions,” Quantum Sci. Technol. 5, 045015 (2020).
[Crossref]

Askarani, M. F.

M. F. Askarani, M. G. Puigibert, T. Lutz, V. B. Verma, M. D. Shaw, S. W. Nam, N. Sinclair, D. Oblak, and W. Tittel, “Storage and reemission of heralded telecommunication-wavelength photons using a crystal waveguide,” Phys. Rev. Appl. 11, 054056 (2019).
[Crossref]

Bartholomew, J. G.

I. Craiciu, M. Lei, J. Rochman, J. M. Kindem, J. G. Bartholomew, E. Miyazono, T. Zhong, N. Sinclair, and A. Faraon, “Nanophotonic quantum storage at telecommunication wavelength,” Phys. Rev. Appl. 12, 024062 (2019).
[Crossref]

D. L. McAuslan, J. G. Bartholomew, M. J. Sellars, and J. J. Longdell, “Reducing decoherence in optical and spin transitions in rare-earth-metal-ion–doped materials,” Phys. Rev. A 85, 032339 (2012).
[Crossref]

Bhaskar, M. K.

M. K. Bhaskar, R. Riedinger, B. Machielse, D. S. Levonian, C. T. Nguyen, E. N. Knall, H. Park, D. Englund, M. Lončar, D. D. Sukachev, and M. D. Lukin, “Experimental demonstration of memory-enhanced quantum communication,” Nature 580, 60–64 (2020).
[Crossref]

Böttger, T.

T. Böttger, C. W. Thiel, R. L. Cone, and Y. Sun, “Effects of magnetic field orientation on optical decoherence in Er3+:Y2SiO5,” Phys. Rev. B 79, 115104 (2009).
[Crossref]

Y. Sun, T. Böttger, C. W. Thiel, and R. L. Cone, “Magnetic g tensors for the 4I15/2 and 4I13/2 states of Er3+:Y2SiO5,” Phys. Rev. B 77, 085124 (2008).
[Crossref]

T. Böttger, Y. Sun, C. W. Thiel, and R. L. Cone, “Spectroscopy and dynamics of Er3+:Y2SiO5 at 1.5µm,” Phys. Rev. B 74, 075107 (2006).
[Crossref]

Brennen, G.

G. Brennen, E. Giacobino, and C. Simon, “Focus on quantum memory,” New J. Phys. 17, 050201 (2015).
[Crossref]

Briegel, H.-J.

H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[Crossref]

Buchler, B. C.

M. Hosseini, B. M. Sparkes, G. Hétet, J. J. Longdell, P. K. Lam, and B. C. Buchler, “Coherent optical pulse sequencer for quantum applications,” Nature 461, 241–245 (2009).
[Crossref]

Businger, M.

M. Businger, A. Tiranov, K. T. Kaczmarek, S. Welinski, Z. Zhang, A. Ferrier, P. Goldner, and M. Afzelius, “Optical spin-wave storage in a solid-state hybridized electron-nuclear spin ensemble,” Phys. Rev. Lett. 124, 053606 (2020).
[Crossref]

Bustard, P. J.

K. A. G. Fisher, D. G. England, J.-P. W. MacLean, P. J. Bustard, K. J. Resch, and B. J. Sussman, “Frequency and bandwidth conversion of single photons in a room-temperature diamond quantum memory,” Nat. Commun. 7, 11200 (2016).
[Crossref]

K. Heshami, D. G. England, P. C. Humphreys, P. J. Bustard, V. M. Acosta, J. Nunn, and B. J. Sussman, “Quantum memories: emerging applications and recent advances,” J. Mod. Opt. 63, 2005–2028 (2016).
[Crossref]

Chan, J.

S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Highly efficient coupling from an optical fiber to a nanoscale silicon optomechanical cavity,” Appl. Phys. Lett. 103, 181104 (2013).
[Crossref]

Chanelière, T.

Chen, H.-S.

Y.-F. Hsiao, P.-J. Tsai, H.-S. Chen, S.-X. Lin, C.-C. Hung, C.-H. Lee, Y.-H. Chen, Y.-F. Chen, I. A. Yu, and Y.-C. Chen, “Highly efficient coherent optical memory based on electromagnetically induced transparency,” Phys. Rev. Lett. 120, 183602 (2018).
[Crossref]

Chen, Y.-C.

Y.-F. Hsiao, P.-J. Tsai, H.-S. Chen, S.-X. Lin, C.-C. Hung, C.-H. Lee, Y.-H. Chen, Y.-F. Chen, I. A. Yu, and Y.-C. Chen, “Highly efficient coherent optical memory based on electromagnetically induced transparency,” Phys. Rev. Lett. 120, 183602 (2018).
[Crossref]

Chen, Y.-F.

Y.-F. Hsiao, P.-J. Tsai, H.-S. Chen, S.-X. Lin, C.-C. Hung, C.-H. Lee, Y.-H. Chen, Y.-F. Chen, I. A. Yu, and Y.-C. Chen, “Highly efficient coherent optical memory based on electromagnetically induced transparency,” Phys. Rev. Lett. 120, 183602 (2018).
[Crossref]

Chen, Y.-H.

J. V. Rakonjac, Y.-H. Chen, S. P. Horvath, and J. J. Longdell, “Long spin coherence times in the ground state and in an optically excited state of 163Er3+:Y2SiO5 at zero magnetic field,” Phys. Rev. B 101, 184430 (2020).
[Crossref]

Y.-F. Hsiao, P.-J. Tsai, H.-S. Chen, S.-X. Lin, C.-C. Hung, C.-H. Lee, Y.-H. Chen, Y.-F. Chen, I. A. Yu, and Y.-C. Chen, “Highly efficient coherent optical memory based on electromagnetically induced transparency,” Phys. Rev. Lett. 120, 183602 (2018).
[Crossref]

Chung, T.-H.

H. Wang, H. Hu, T.-H. Chung, J. Qin, X. Yang, J.-P. Li, R.-Z. Liu, H.-S. Zhong, Y.-M. He, X. Ding, Y.-H. Deng, Q. Dai, Y.-H. Huo, S. Höfling, C.-Y. Lu, and J.-W. Pan, “On-demand semiconductor source of entangled photons which simultaneously has high fidelity, efficiency, and indistinguishability,” Phys. Rev. Lett. 122, 113602 (2019).
[Crossref]

Cirac, J. I.

H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[Crossref]

Cone, R. L.

T. Böttger, C. W. Thiel, R. L. Cone, and Y. Sun, “Effects of magnetic field orientation on optical decoherence in Er3+:Y2SiO5,” Phys. Rev. B 79, 115104 (2009).
[Crossref]

Y. Sun, T. Böttger, C. W. Thiel, and R. L. Cone, “Magnetic g tensors for the 4I15/2 and 4I13/2 states of Er3+:Y2SiO5,” Phys. Rev. B 77, 085124 (2008).
[Crossref]

T. Böttger, Y. Sun, C. W. Thiel, and R. L. Cone, “Spectroscopy and dynamics of Er3+:Y2SiO5 at 1.5µm,” Phys. Rev. B 74, 075107 (2006).
[Crossref]

Craiciu, I.

I. Craiciu, M. Lei, J. Rochman, J. M. Kindem, J. G. Bartholomew, E. Miyazono, T. Zhong, N. Sinclair, and A. Faraon, “Nanophotonic quantum storage at telecommunication wavelength,” Phys. Rev. Appl. 12, 024062 (2019).
[Crossref]

E. Miyazono, I. Craiciu, A. Arbabi, T. Zhong, and A. Faraon, “Coupling erbium dopants in yttrium orthosilicate to silicon photonic resonators and waveguides,” Opt. Express 25, 2863–2871 (2017).
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Dai, Q.

H. Wang, H. Hu, T.-H. Chung, J. Qin, X. Yang, J.-P. Li, R.-Z. Liu, H.-S. Zhong, Y.-M. He, X. Ding, Y.-H. Deng, Q. Dai, Y.-H. Huo, S. Höfling, C.-Y. Lu, and J.-W. Pan, “On-demand semiconductor source of entangled photons which simultaneously has high fidelity, efficiency, and indistinguishability,” Phys. Rev. Lett. 122, 113602 (2019).
[Crossref]

Dajczgewand, J.

de Riedmatten, H.

B. Lauritzen, J. Minář, H. de Riedmatten, M. Afzelius, and N. Gisin, “Approaches for a quantum memory at telecommunication wavelengths,” Phys. Rev. A 83, 012318 (2011).
[Crossref]

B. Lauritzen, J. Minář, H. de Riedmatten, M. Afzelius, N. Sangouard, C. Simon, and N. Gisin, “Telecommunication-wavelength solid-state memory at the single photon level,” Phys. Rev. Lett. 104, 080502 (2010).
[Crossref]

I. Usmani, M. Afzelius, H. de Riedmatten, and N. Gisin, “Mapping multiple photonic qubits into and out of one solid-state atomic ensemble,” Nat. Commun. 1, 12 (2010).
[Crossref]

M. Afzelius, C. Simon, H. de Riedmatten, and N. Gisin, “Multimode quantum memory based on atomic frequency combs,” Phys. Rev. A 79, 052329 (2009).
[Crossref]

S. R. Hastings-Simon, B. Lauritzen, M. U. Staudt, J. L. M. van Mechelen, C. Simon, H. de Riedmatten, M. Afzelius, and N. Gisin, “Zeeman-level lifetimes in Er3+:Y2SiO5,” Phys. Rev. B 78, 085410 (2008).
[Crossref]

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multimode memories,” Phys. Rev. Lett. 98, 190503 (2007).
[Crossref]

Deng, Y.-H.

H. Wang, H. Hu, T.-H. Chung, J. Qin, X. Yang, J.-P. Li, R.-Z. Liu, H.-S. Zhong, Y.-M. He, X. Ding, Y.-H. Deng, Q. Dai, Y.-H. Huo, S. Höfling, C.-Y. Lu, and J.-W. Pan, “On-demand semiconductor source of entangled photons which simultaneously has high fidelity, efficiency, and indistinguishability,” Phys. Rev. Lett. 122, 113602 (2019).
[Crossref]

Deotare, P. B.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[Crossref]

Dibos, A. M.

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Quantum Sci. Technol. (1)

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[Crossref]

Other (2)

C. Liu, T.-X. Zhu, M.-X. Su, Y.-Z. Ma, Z.-Q. Zhou, C.-F. Li, and G.-C. Guo, “On-demand quantum storage of photonic qubits in an on-chip waveguide,” arXiv:2009.01796 (2020).

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Supplementary Material (1)

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Supplement 1       Supplemental Document

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Figures (4)

Fig. 1.
Fig. 1. Multifunctional quantum storage device. (a) Schematic of device functionality showing the optical resonator (pink), electrodes (blue and red), and memory output. (b)–(d) Hybrid optical resonator comprised of an amorphous silicon ( $\alpha {\rm Si}$ ) waveguide on $^{167}{{\rm Er}^{3 +}}$ : ${{\rm Y}_2}{{\rm SiO}_5}$ with photonic crystal mirrors on either end. (b) Cross section of waveguide (black outline) showing 2D finite element simulation of the TM waveguide mode. The purple-white gradient indicates the ${E_z}$ component of the optical field. (c) Band diagram showing waveguide mode (solid red line), band gap of a photonic crystal mirror (solid blue lines), and the design frequency of 195 THz (dashed red line). Blue areas indicate the ${{\rm Y}_2}{{\rm SiO}_5}$ light cone containing extended modes propagating in bulk ${{\rm Y}_2}{{\rm SiO}_5}$ (both sides for photonic crystal, left side only for waveguide). (d) Scanning electron micrograph showing a grating coupler and photonic crystal mirror including tapered sections on either side to reduce scattering [34]. (e)–(g) 3D finite element simulation of on-chip electrodes. (e)–(f) 2D slice at $z = 0$ showing electric potential (blue-red gradient) in the (e) parallel and (f) quadrupole biasing configurations. (g) Electric field ${E_y}(x)$ along the optical resonator in the parallel (green solid line) and quadrupole (orange solid line) configurations; ${E_y}(x)$ was measured at $z = 0$ , $y = 0$ , ${-}56\,\unicode{x00B5}{\rm m} \lt x \lt 56\,\unicode{x00B5}{\rm m}$ [green and orange lines in (e) and (f)]; dashed lines indicate ideal parallel (green) and quadrupole (orange) electric field distributions. (h) Optical micrograph showing an optical resonator, gold electrodes, and gold wires for electrical contact.
Fig. 2.
Fig. 2. AFC storage with dynamic memory time control. (a) Pulse sequence (not to scale, details in main text). (b) Atomic frequency comb. Cavity reflectance (black points) and fit to six Gaussians (solid black lines). All teeth are fit together, with the finesse fixed to the value from (d). Detuning is measured from 194,822 GHz. The gray Gaussian with a dashed outline represents the input pulses in frequency space. c) Emission of stored light at different times ${t_{{\rm memory}}} = \frac{m}{\Delta}$ . Partly reflected input pulse are shown in gray at $t = 0$ . On-demand memory outputs are shown in blue (darkest shade). Subsequent emissions (green to red) are discussed in the main text. Electric pulses are not shown. (d) Energy emitted in the time bin at $t = \frac{m}{\Delta}$ for each value of $m$ . Black data points represent the normalized counts when all previous emissions are suppressed with electric pulses [blue pulses in (c)]. Gray data points represent normalized counts when previous emissions are not suppressed, meaning no electric pulses are used [all pulses on line $m = 1$ in (c)]. The error bars, representing $\sqrt {{N_{{\rm counts}}}}$ , are smaller than the markers. The solid line is a fit to theory, fitting only for comb finesse.
Fig. 3.
Fig. 3. AFC storage with frequency control. (a) Pulse sequence (not to scale; details in main text). (b)–(c) Examples of AFC output pulses with (green, lighter) and without (blue, darker) a frequency shift. The filled-in area is a Gaussian fit to the data (circles). Detuning is measured from 194,822 GHz. Frequency shifts of (b) 9 MHz and (c) 30 MHz are shown. (d) The output detuning as a function of electric field applied during emission. Circles are the centers of Gaussian fits [as shown in (b)–(c)]. The error bars, which are smaller than the markers, are 95% confidence intervals for those fits. The solid line is a linear fit to the data, yielding a slope of $13.0 \pm 0.3$ kHz/(V/cm), similar to the Stark shift value measured by hole-burning spectroscopy (see Supplement 1 Section 1).
Fig. 4.
Fig. 4. AFC storage with bandwidth control. (a) Pulse sequence (not to scale; details in main text). (b) AFC storage with (bottom) and without (top) bandwidth broadening. Colored areas are Gaussian fits to photon counts data (circles) from which widths are extracted. The partially reflected input pulse with FWHM 77.4 ns (5.7 MHz FWHM in the frequency domain) is shown in gray (lighter color) in both traces at $t = 0$ , demagnified by a factor of ${10^3}$ . The top trace shows the case without bandwidth broadening ${E_{{\rm max}}}(t = 630\,{\rm ns}) = {E_{{\rm max}}}(t = 0) = 0.67\;{\rm kV/cm}$ , where the width of the output (blue, darker) is $77.1 \pm 2.0\;{\rm ns}$ ( $5.7 \pm 0.1\;{\rm MHz} $ ). The bottom trace shows the maximum bandwidth broadening ${E_{{\rm max}}}(t = 630\,{\rm ns}) = 4 \times {E_{{\rm max}}}(t = 0) = 2.8\;{\rm kV/cm}$ , where the width of the output (blue, darker) is $24.3 \pm 0.5\;{\rm ns}$ ( $18.1 \pm 0.4\;{\rm MHz} $ ). Insets show schematics of electrode pulse sequences. (c) Bandwidth of pulses as a function of the $E_{{\rm max}}^{{\rm output}}$ . In all cases, $E_{{\rm input}}^{{\rm max}} = 0.67\;{\rm kV/cm}$ . Filled black circles are FWHM data. The error bars, which are smaller than the markers, represent 95% confidence intervals from fits. The unfilled gray circles are simulation data (see main text and Supplement 1 Section 5).

Equations (1)

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| Ψ = j = 1 N i o n s c j e i 2 π ( f j + δ f j ( t ) ) t e i k r j | 0 1 j 0 N .

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